Proability estimation usind a multinominal logistic function

A multinomial logistic model is used for estimating the probabilities of k mutually exclusive and exhaustive events as a function of p independent variables. The parameters are estimated by maximum likelihood involving non-linear iterative techniques. Careful attention is given to the computational procedure which involves the estimation of (k − 1) (p + 1) parameters. The prediction of the probability of respiratory distress syndrome (RDS) in human newborns is presented as an example, It was found that initial estimates obtained from the linear discriminant functions often were far from the maximum likelihood solution and that simple Newton-Raphson procedures often diverge. The final algorithm has been tested on many data sets and has always converged.